diff --git a/src/project_surface_points_on_poly.cc b/src/project_surface_points_on_poly.cc
index 0dc3899..5375bda 100644
--- a/src/project_surface_points_on_poly.cc
+++ b/src/project_surface_points_on_poly.cc
@@ -41,27 +41,27 @@ vtkTypeBool ProjectSurfacePointsOnPoly::RequestData(
 	vtkInformationVector **inputVector,
 	vtkInformationVector *outputVector) {
 	(void) request;
-	vtkUnstructuredGrid* us = vtkUnstructuredGrid::GetData(inputVector[0]);
-	vtkPolyData* pd = vtkPolyData::GetData(inputVector[1]);
+	vtkUnstructuredGrid* tetMesh = vtkUnstructuredGrid::GetData(inputVector[0]);
+	vtkPolyData* polyMesh = vtkPolyData::GetData(inputVector[1]);
 	vtkUnstructuredGrid* output =
 		vtkUnstructuredGrid::GetData(outputVector);
 
-	output->CopyStructure(us);
-	output->GetPointData()->PassData(us->GetPointData());
-	output->GetCellData()->PassData(us->GetCellData());
+	output->CopyStructure(tetMesh);
+	output->GetPointData()->PassData(tetMesh->GetPointData());
+	output->GetCellData()->PassData(tetMesh->GetCellData());
 
 	/* Generate cell links, these tell us which cell a point belongs to. */
 	vtkNew<vtkStaticCellLinks> links;
-	links->BuildLinks(pd);
+	links->BuildLinks(polyMesh);
 
 	vtkNew<vtkKdTree> kdTree;
-	kdTree->BuildLocatorFromPoints(pd->GetPoints());
+	kdTree->BuildLocatorFromPoints(polyMesh->GetPoints());
 
-	vtkIdTypeArray *externalPoints =
-		vtkIdTypeArray::SafeDownCast(us->GetFieldData()->GetArray("external_points"));
-	for (vtkIdType i = 0; i < externalPoints->GetNumberOfTuples(); i++) {
+	vtkIdTypeArray *surfacePoints =
+		vtkIdTypeArray::SafeDownCast(tetMesh->GetFieldData()->GetArray("surface_points"));
+	for (vtkIdType i = 0; i < surfacePoints->GetNumberOfTuples(); i++) {
 		double p[3];
-		us->GetPoint(externalPoints->GetTuple1(i), p);
+		tetMesh->GetPoint(surfacePoints->GetTuple1(i), p);
 		double dist2;
 		vtkIdType closest = kdTree->FindClosestPoint(p, dist2);
 		vtkIdType *cellIds = links->GetCells(closest);
@@ -73,7 +73,7 @@ vtkTypeBool ProjectSurfacePointsOnPoly::RequestData(
 		for (vtkIdType j = 0; j < nCells; j++) {
 			vtkIdType cellId = cellIds[j];
 			double direction[3];
-			double dist = pointTriangleDistance(p, pd->GetCell(cellId), direction);
+			double dist = pointTriangleDistance(p, polyMesh->GetCell(cellId), direction);
 			/* Find the closest one. */
 			if (dist < min_dist) {
 				min_dist = dist;
@@ -85,8 +85,8 @@ vtkTypeBool ProjectSurfacePointsOnPoly::RequestData(
 
 		vtkMath::MultiplyScalar(min_direction, min_dist);
 		vtkMath::Subtract(p, min_direction, p);
-		us->GetPoints()->SetPoint(externalPoints->GetTuple1(i), p);
-		us->Modified();
+		tetMesh->GetPoints()->SetPoint(surfacePoints->GetTuple1(i), p);
+		tetMesh->Modified();
 	}
 
 	return true;
diff --git a/src/surface_points_filter.cc b/src/surface_points_filter.cc
index 4579d23..e87f625 100644
--- a/src/surface_points_filter.cc
+++ b/src/surface_points_filter.cc
@@ -52,7 +52,7 @@ vtkTypeBool SurfacePointsFilter::RequestData(
 
 	/* Create an array to store the IDs of external points. */
 	vtkNew<vtkIdTypeArray> externalPoints;
-	externalPoints->SetName("external_points");
+	externalPoints->SetName("surface_points");
 	externalPoints->SetNumberOfComponents(1);
 	vtkNew<vtkIntArray> isExternal;
 	isExternal->SetName("bl");